Question

On Friday afternoon, 560 people went to the local theater for the matinee. Youth tickets cost 5.75 and adult tickets cost 8.50. If the theater's sales receipts totaled 3907.50, how many youth tickets were bought on friday afternoon?

Answer 1

310 youth tickets were sold

Solution:

Let "a" be the number of youth tickets sold

Let "b" be the number of adult tickets sold

Cost of 1 youth ticket = $ 5.75

Cost of 1 adult ticket = $ 8.50

On Friday afternoon, 560 people went to the local theater for the matinee

Therefore,

a + b = 560 ---------- eqn 1

The theater's sales receipts totaled 3907.50

Therefore, we frame a equation as:

number of youth tickets x Cost of 1 youth ticket + number of adult tickets x Cost of 1 adult ticket = 3907.50

$a \times 5.75 + b \times 8.50 = 3907.50\\\\5.75a + 8.50b = 3907.50 --------- eqn 1$

From eqn 1,

a = 560 - b --------- eqn 2

Substitute eqn 2 in eqn 1

5.75(560 - b) + 8.50b = 3907.50

3220 - 5.75b + 8.50b = 3907.50

2.75b = 3907.50 - 3220

2.75b = 687.5

Divide both sides of equation by 2.75

b = 250

Substitute b = 250 in eqn 3

a = 560 - 250

a = 310

Thus 310 youth tickets were sold